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The commutative property states that the order in which two values are summed does not affect the resulting sum. For example, 2 + 3 = 5 and 3 + 2 = 5.

The associative property states that when three or more numbers are being grouped before addition, the grouping order does not effect the sum. For example, (2 + 3) + 4 = 9 and 2 + (3 + 4) = 9.

The distributive property states that the sum of two numbers multiplied by another number is equal to each addend multiplied by that third number and then summed. For example, 6 x (2 + 1) = 18 and 6 x 2 + 6 x 1 = 18.

The identity property states that the sum of any value and zero is that same value. For example, 3 + 0 = 3.

The additive inverse property states that for any value, there is an equal, opposite value, such that, when the two are summed, they equal zero. For example, 2 + -2 = 0.

Moreover, since subtraction may be rewritten as addition with negative numbers, subtraction follows the same basic properties as addition once rewritten.